1600’s. The early settlers.

Before the settlement of East Hampton by Europeans, Native Americans inhabited the beautiful woodlands and coastlands here. Many of the place names in East Hampton are of Indian origin. The Montaukett Tribe of the Algonquin Indians, gave their name to what is now called Montauk. “Paumanok” celebrated by the poet Walt Whitman, was the original Indian name for Long Island.

Sea-beauty! stretch'd and basking!
One side thy inland ocean laving, broad, with copious commerce, steamers, sails,
And one the Atlantic's wind caressing, fierce or gentle--mighty hulls dark-
gliding in the distance. Isle of sweet brooks of drinking-water--
healthy air and soil! Isle of the salty shore and breeze and brine!
From “Paumanok” by Walt Whitman (1819-1892)

The official date of the European settlement of East Hampton is 1648, when 34 Puritan families (who had originally migrated from England to Massachusetts to Southampton) continued to migrate onward, settling in what is now known as East Hampton. These early settlers purchased shares of land from the governors of the New Haven and Connecticut Colonies, who themselves had purchased 31,000 acres of land from the Montaukett tribe.
These ties to New England were to prove enduring: In 1653, East Hampton adopted the laws of Connecticut Colony; in 1657 it united with Connecticut Colony. In 1664, when the Dutch settlers in New York surrendered their colony of New York to the English, the Duke of York claimed jurisdiction over the whole of Long Island, and the residents of East Hampton and Southampton eventually accepted that jurisdiction (but not without protest.) Even today, the town, especially the village, retains some of the look and feel of its New England roots. The original layout of the 34 settler homes was typical of Puritan New England towns: a broad common about a mile in length flanked by home lots of eight to twelve acres each. In East Hampton, this “common” was the land north of Town Pond.
Originally, the name these early settlers gave their new home was Maidstone, after a town in Kent England, from which many of them originally hailed. Today, the echo of that name is still heard here in establishments such as the Maidstone Arms hotel and the Maidstone Club, and in public spaces such as Maidstone Park.
However, even before this official settlement date of 1648, an Englishman, Lion Gardiner, had entered into agreement with Chief Wyandanch of the Montaukett Tribe to purchase the island that would eventually bear his name: Gardiner’s Island. The purchase was made in 1639, reputedly for a few blankets, a “large black dog,” and some gunpowder. In time, after the Revolutionary War, Gardiner’s Island was to become part of East Hampton.

Most the above text was lifted from various web sites including East Hampton Historical Society.